A Three-Dimensional Electromagnetic Shell Finite Element for Coupled Vector-Scalar Potential Formulations

In many eddy current problems solved by FEM, meshing of the skin depth leads to CAD difficulties and large computing. In order to avoid such problems, one currently use surface impedance conditions: boundary conditions in the case of massive conductors or transmission conditions or shell elements in the case of thin conducting layers. In this paper, we propose a new shell finite element with arbitrary thickness that is compatible with the $({\rm A}-\varphi)$ and $({\rm T}-\Omega)$ formulations. Both formulations exist in some general purpose finite element electromagnetic codes like Code_Carmel3D. To validate the approach, two elementary numerical tests are treated.